Suppose that, during the first year after its hatching, the weight of a duck increases at a rate proportional to its weight. The duckling weighed 2 pounds when it was hatched and 3.5 pounds at age 4 months. How many pounds will the bird weigh at age 6 months

4.25 pound

Step-by-step explanation:

Ratio is the quantitative relation between two amounts, which is being compared. In this question we are considering the ratio of weight to time consumed.

At the age 0

Weight = 2 pound

At the age 4 months

Weight = 3.5 pound

Proportion of Change = Change in Weight / Change in time = (3.5 - 2) / (4-0) = 1.5 / 4 = 0.375 pound per month

Weight after 6 months = 2 + (6 x 0.375 pond per month) = 4.25 pound